### Step 1: Total number of ways to choose 3 experts from 15:
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- ### Step 1: Total number of ways to choose 5 buses from 15:
- ### Step 2: Favorable outcomes — at least two of each color
- ### Step 3: Compute the probability
- ### Step 2: Favorable outcomes — at least one from each profession
- -\frac{2}{7} \leq k \leq \frac{97}{7} \approx 13.857
- $ n = 1 $: $ 1^2 = 1 \equiv 1 \pmod{12} $ ✅
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